There is a certain village in Japan, situated in a very low valley, and yet on the Spring Equinox, the sun is nearer to the inhabitants at noon, by 3,000 miles and upwards, than when it either rises or sets. In what part of the country is the village situated?

The valleys and mountains are negligible compared with the size of the earth.

Taking 4,000 miles as the radius of the earth, the sun must be up at least arcsin(3/4), or 48.6 degrees above the horizon for the location to be at least 3,000 miles closer to the sun at noon than at sunrise or set.  So the village must be at or south of 90-48.6 = 41.4 degrees north latitude.

During seasons when the sun is north of the equator, more such villages will experience the effect, so that at the Summer Solstice, this effect reaches 41.4 + 23.4 = 64.8 degrees north. At the Winter solstice, it would reach only 41.4 - 23.4 = 18 degrees north -- not far enough north for any part of Japan.

Posted by Charlie on 2006-03-01 11:07:31